Centroid, incentre and orthocentre
Two-dimensional geometry · Mathematics
Study notes
Q: Triangle vertices (0,0), (6,0), (3,6). Find centroid and orthocentre. Centroid G = ((0+6+3)/3, (0+0+6)/3) = (3, 2). Altitudes: from (3,6) vertical (base horizontal): x = 3. From (0,0): altitude ⊥ opposite side. Opposite side from (6,0) to (3,6): slope = -2, so altitude slope = 1/2: y = x/2. At x=3: y=1.5. H = (3, 1.5).